# MCQ Questions for Class 12 Maths Chapter 4 Determinants with answers

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Below you will find MCQ Questions of Chapter 4 Determinants Class 12 Maths Free PDF Download that will help you in gaining good marks in the examinations and also cracking competitive exams. These Class 12 MCQ Questions with answers will widen your skills and understand concepts in a better manner.

# MCQ Questions for Class 12 Maths Chapter 4 Determinants with answers

1. If A is a square matrix of order 3 and |A| = 5 then |3A| = ?​

(a) 135

(b) 45

(c) 15

(d) 32

► (a) 135

2. Inverse of a matrix A exists, if​

(a) | A | = 0

(b) Matrix A is non-singular

(c) Matrix A is singular

(d) AT = A

► (b) Matrix A is non-singular

3. If the value of , then the value of (a) -7

(b) 14

(c) 7

(d) -14

► (c) 7

4. If matrix A = and A2 + aA + b = O, then the values of a and b are:

(a) a = – 6, b = 2

(b) a = 6, b = – 2

(c) a = 6, b = 2

(d) a = – 6, b = – 2

► (a) a = – 6, b = 2

5. If , then the relation between x and y is

(a) y = -3x

(b) x = 3y

(c) x = -3y

(d) y = 3x

► (d) y = 3x

6. (a) −2(a+b+c)3

(b) 2(a+b+c)2

(c) 4(a+b+c)3

(d) None of these

► (d) None of these

7. The minor Mij of an element aij of a determinant is defined as the value of the determinant obtained after deleting the​

(a) jth row of the determinant

(b) ith column and jth row of the determinant

(c) ith row and jth column of the determinant

(d) ith row of the determinant

► (c) ith row and jth column of the determinant

8. If A and B are any 2 × 2 matrices , then det. (A+B) = 0 implies

(a) det A = 0 and det B = 0

(b) det A = 0 or det B = 0

(c) detA + det B = 0

(d) None of these

► (d) None of these

9. If A = , and |3A| = k|A|, then the value of k is

(a) 27

(b) 1

(c) 25

(d) 4

► (a) 27

10. A system of linear equations AX = B is said to be inconsistent, if the system of equations has​

(a) Trivial Solution

(b) Infinite Solutions

(c) No Solution

(d) Unique Solutions

► (c) No Solution

11. If A is a square matrix of order 3 and |A| = 7 then |AT| =​

(a) 7

(b) 21

(c) 1/7

(d) 3

► (a) 7

12. The value of the determinant is

(a) 4

(b) 0

(c) -1

(d) 1

► (b) 0

13. System of equations AX = B is inconsistent if​

(a) │B│ = 0

(b) (adj A) B = 0

(c) (adj A) B ≠ 0

(d) │A│ ≠ 0

► (c) (adj A) B ≠ 0

14. Points (a,a,c),(1,0,1) and (c,c,b) are collinear if​

(a) a,b,c in GP

(b) a,b,c in AP

(c) C2 = ab

(d) C = ab

► (c) C2 = ab

15. If I3 is the identity matrix of order 3 , then 13−1 is

(a) 0

(b) 3I3

(c) I3

(d) None of these

► (c) I3

16. The following system of equations has

x + 3y + 3z = 2

x + 4y + 3z = 1

x + 3y + 4z = 2​

(a) Infinite Solution

(b) Trivial Solution

(c) Unique Solution

(d) No Solution

► (c) Unique Solution

17. In a third order determinant, each element of the first column consists of sum of two terms, each element of the second column consists of sum of three terms and each element of the third column consists of sum of four terms. Then it can be decomposed into n determinants, where n has value

(a) 1

(b) 9

(c) 24

(d) 16

► (c) 24

18. The value of determinant (a) zero

(b) 8

(c) 1

(d) 10

► (a) zero

19. The system of equations kx + 2y – z = 1,

(k – 1)y – 2z = 2

(k + 2)z = 3 has a unique solution, if k is

(a) – 1

(b) – 2

(c) 1

(d) 0

► (a) – 1

20. If A is a symmetric matrix, then At =

(a) A

(b) |A|

(c) 0

(d) diagonal matrix

► (a) A

21. If A’ is the transpose of a square matrix A , then

(a) |A| ≠ |A′|

(b) |A|+|A′| = 0

(c) |A| = |A′|

(d) None of these

► (c) |A| = |A′|

22. If A B be two square matrices such that AB = O, then

(a) Det.B = 0

(b) BA

(c) Det. A = 0 or Det. B = 0

(d) Det. = A = 0

► (c) Det. A = 0 or Det. B = 0

Hope the given MCQ Questions will help you in cracking exams with good marks. These Determinants MCQ Questions will help you in practising more and more questions in less time.

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